Why do prices jump? by Jean-Philippe Bouchaud

After years of investigation, we still aren’t sure, says Jean-Philippe Bouchaud

Key points Summary Q&A

• Price changes are heavy‑tailed, with extreme jumps occurring far more often than a Gaussian model predicts.
• Many large, rapid moves have no identifiable news catalyst, so news alone cannot explain most jumps.
• Volatility patterns suggest that instances of multiple stocks jumping simultaneously are due to one stock jumping, with all others following suit.

These summaries are generated by an LLM, but edited by humans.

It is well known that the distribution of price changes is heavy-tailed, with extreme events – so-called ‘jumps’ – occurring with far greater frequency than the Black-Scholes, Gaussian framework would predict. Even the most sophisticated path-dependent, stochastic volatility models struggle to account for such tails. To put this into context: individual stocks tend to experience moves larger than four-sigma at the one-minute level every few days – roughly once every 800 observations – whereas under a Gaussian prior, such an event would be expected only once every 16,000 observations.

Where do all these jumps come from? One natural explanation, rooted in efficient market theory, is that news triggers them. The problem is that there is simply not enough idiosyncratic news to explain why any particular stock jumps when it does. Moreover, when financial news feeds are synchronised with price changes, a substantial fraction of large, rapid moves turn out to have no identifiable news catalyst whatsoever. 

A similar observation was reported by Cutler, Poterba and Summers as far back as 1988, at daily frequencies and for the S&P 500 as a whole. In their words: “The evidence that large market moves often occur on days without any identifiable major news releases casts doubt on the view that stock price movements are fully explicable by news.” This conundrum, of course, is nothing other than the famous ‘excess volatility puzzle’ in another guise.

What else, then, might explain the appearance and frequency of such jumps? One alternative hypothesis is that of endogenous liquidity crises. The argument runs as follows: market-making is an inherently risky business. When volatility rises for reasons opaque to market-makers, they respond by widening bid/ask spreads to protect themselves against adverse selection. This, however, can trigger an unstable feedback loop: the cancellation of limit orders amplifies the market impact of incoming market orders, driving volatility still higher. 

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A stylised mathematical model captures this mechanism and indeed predicts that liquidity crises – and therefore price jumps – can arise spontaneously, as the cumulative result of individually innocuous events. A key signature of this picture is that volatility should increase before the jump occurs. This stands in contrast to news-induced jumps, where volatility should be flat ahead of the announcement (since, absent leakage, no-one can anticipate it) and spike sharply only after.

This volatility asymmetry can, in fact, be detected in the data. Analysing a large collection of jumps, one finds a correlation between news-induced jumps and backloaded volatility, while no-news jumps appear more symmetric. A more recent study using wavelet analysis on one-minute binned data has uncovered further, unexpected categories: jumps followed by silent volatility, trending jumps, contrarian jumps, and others. Meanwhile, the size distribution of ‘co-jumps’ – stocks that jump simultaneously – reveals a power-law shape reminiscent of the distribution of avalanches and other contagion processes. This observation strongly suggests that while some co-jumps are triggered by common macro news, many co-jumps are actually due to one stock jumping for whatever reason, with all others following suit.

To understand what is truly going on, one must zoom into the high-frequency dynamics of the order book – a project we are currently pursuing with Ana Bugaenko, Michael Benzaquen and Damien Challet. Are prices driven by fundamentals, or by the subtle interplay between order flow and liquidity provision? These questions carry profound implications at both the macro level (what are markets really telling us about the economy?) and the micro level (can one design mechanisms that make markets less prone to recurring dislocations?). 

Despite years of investigation, we are still not sure. But the final answer will surely be relevant for market participants and regulators alike: stabilising unstable markets is worth the effort.

Jean-Philippe Bouchaud is chairman and head of research at Capital Fund Management

Editing by Alex Krohn